ERKN methods for long-term integration of multidimensional orbital problems
ERKN methods for long-term integration of multidimensional orbital problems
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DOI：
10.1016/j.apm.2012.05.021
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发表时间：
2013-02
影响因子：
5
通讯作者：
Xinyuan Wu;Bin Wang-;Kai Liu;Hua Zhao
中科院分区：
文献类型：
--
作者：
Xinyuan Wu;Bin Wang-;Kai Liu;Hua Zhao
本文介绍了多维轨道问题长期积分的ERKN方法。对于具有M∈Rm×m的一般多维摄动振子y“+my=f(t，y)，吴等人提出了扩展的龙格-库塔-奈斯特伦方法。[X.Wu，X.You，W.Shiw，B.Wang，ErkN解二阶振动微分方程组的积分器，计算机.太棒了。交警。181(2010)1873-1887]。这些方法精确地积分了多维非摄动振子，并且在摄动力很小时是非常有效的。本文主要研究ERKN方法在多维轨道问题中的应用。数值实验表明，对于多维轨道问题的长期积分，多维ERKN方法比科学文献中提出的高质量程序更有效。特别是，当轨道问题是哈密顿系统时，辛ERKN方法很好地保持了哈密顿量，并且在相同计算量的情况下具有比高质量代码更好的精度。
This paper is devoted to introducing ERKN methods for long-term integration of multidimensional orbital problems. For the general multidimensional perturbed oscillators y″+My=f(t,y) with M∈Rm×m, the extended Runge–Kutta–Nyström (ERKN) methods are proposed by Wu et al. [X. Wu, X. You, W. Shi, B. Wang, ERKN integrators for systems of oscillatory second-order differential equations, Comput. Phys. Commun. 181 (2010) 1873–1887]. These methods exactly integrate the multidimensional unperturbed oscillators and are highly efficient when the perturbing forces are small. In this paper, we pay attention to the applications of ERKN methods to multidimensional orbital problems. Numerical experiments accompanied demonstrate that for long-term integration of multidimensional orbital problems the multidimensional ERKN methods are more efficient compared with high-quality codes proposed in the scientific literature. In particular, when an orbital problem under consideration is a Hamiltonian system, the symplectic ERKN methods preserve the Hamiltonian very well, and has better accuracy than the high-quality codes with the same computational cost.